Binary stellar systems, contain two stars orbiting their common centre of mass under the effect of their mutual gravitational attraction. Binaries are very common in nature: about two thirds of Sun-like stars are found in binary systems. Many interesting astronomical objects are formed from mass-transfer binaries, including cataclysmic variables, X-ray binaries and type IA supernovae.

For binaries undergoing equilibrium mass transfer in circular binaries the theory of mass transfer is well-established. If a star overfills its Roche Lobe, the potential surface that connects both stars, then matter will flow from one star to the other. However, many systems undergo non-equillibrium mass transfer. Eccentric binaries come in and out of contact on each orbit, transferring mass only during the closest approach. Many stars first transfer mass during the red giant phase, when they are large cool stars up to 1000 times the size of the Sun. This mass transfer is unstable, and leads to a common envelope of low density gas surrounding both stars. This process in inherently non-equilibrium and cannot be followed within the Roche formalism.

To follow non-equilibrium mass transfer in binary systems we have developed a new extension to SPH, a particle-based Lagrangian hydrodynamic technique. In order to model typical mass transfer rates where as little as one part in 10¹² of the star's mass is transferred during each closest approach we have constructed a two-phase system. A layer of light oil particles floats on top of the dense water particles that dominate the mass of the star. The details of the model are described by Church et al. (2009).